However, if the sine wave is applied to a nonlinear circuit, the resulting distortion creates harmonics; frequency components at integer multiples nf of the fundamental frequency f. The distorted signal can be described by a Fourier series in f. The nonzero ck represent the generated harmonics.
From a conversion efficiency standpoint, the nonlinear circuit should maximize the coefficient for the desired harmonic and minimize the others.
YIG multipliers often want to select an arbitrary harmonic, so they use a stateful distortion circuit that converts the input sine wave into an approximate impulse train.
[1] Sometimes the frequency multiplier circuit will adjust the width of the impulses to improve conversion efficiency for a specific harmonic.
Generating a large number of useful harmonics requires a fast nonlinear device, such as a step recovery diode.
The step recovery diode impulse generator is driven at a subharmonic of the desired output frequency.
In transmitting circuits many of the amplifying devices (vacuum tubes or transistors) operate nonlinearly and create harmonics, so an amplifier stage can be made a multiplier by tuning the tuned circuit at the output to a multiple of the input frequency.
Usually the power (gain) produced by the nonlinear device drops off rapidly at the higher harmonics, so most frequency multipliers just double or triple the frequency, and multiplication by higher factors is accomplished by cascading doubler and tripler stages.
An electric-field driven micromechanical cantilever resonator is one of the most fundamental and widely studied structures in MEMS, which can provide a high Q and narrow bandpass filtering function.
The inherent square-law nonlinearity of the voltage-to-force transfer function of a cantilever resonator's capacitive transducer can be employed for the realization of frequency doubling effect.
A voltage controlled oscillator (VCO) is initially tuned roughly to the range of the desired frequency multiple.
In some PLLs the reference frequency may also be divided by an integer multiple before being input to the phase comparator.
This can be accomplished in a different manner by periodically changing the integer value of an integer-N frequency divider, effectively resulting in a multiplier with both whole number and fractional component.
[failed verification] Fractional-N synthesizers provide an effective means of achieving fine frequency resolution with lower values of N, allowing loop architectures with tens of thousands of times less phase noise than alternative designs with lower reference frequencies and higher integer N values.